Sofia Coppola … 'It sounded like it had all the elements for a fun pop movie.' Photograph: Thomas Laisne

A mildly spooky thing happens while I'm at home preparing my questions the night before meeting Sofia Coppola: Nino Rota's theme music for The Godfather comes on the radio. Not only did Coppola's father write and direct the movie, but it marked her own on-screen debut. She's there at the centre of the climactic baptism scene, a nipper still in nappies, oblivious to the innovative cross-cutting going on all around her. Now 42, she's a notoriously reserved interviewee, so I know this is just the ticket to bridge those awkward few moments between the handshake and the opening question. Obviously it would be a more arresting ice-breaker if the radio had been tuned to Kerrang! rather than Classic FM when the Godfather theme kicked in, or if it hadn't been switched on at all, but I decide to give it a go anyway. "Oh, that's funny," she says faintly when I tell her. I bet you get the Godfather music played all the time when you go into restaurants, I say, pressing on needlessly. But I've already lost her. "Oh Scott," she calls to her assistant as he leaves, "will you just – yeah – sorry, will you ring the doorbell first when you – yeah – thanks." No matter. We'll connect eventually, I'm sure.

Then there are those Coppola films concerning dislocated teenagers stranded on the outside trying to get in, such as her 1999 debut, The Virgin Suicides or her latest, The Bling Ring, which stars Emma Watson as one of five real-life Los Angeles friends who burgled the homes of celebrities in the Hollywood Hills. As well as being an indictment of celebrity culture, their crimes were facilitated by it: without copy-hungry websites reporting when precisely Paris Hilton was going to be out partying, or where Orlando Bloom was going to be filming his new movie, the thieves would never have known when to strike. A few clicks later and they had found the properties, as well as the best route in. Many of the victims had not switched on their high-tech security systems. Paris Hilton had even left a key under the mat. (Rather adorably, Hilton has a cameo in the film, and allowed Coppola to shoot in the actual home that was burgled.)

"I didn't pay much attention when I heard about the case on the news," Coppola explains. She has medium-length chestnut hair and a blue short-sleeved blouse with dainty white collars. She talks incredibly fast but also very gently – so much so that when I play back the tape it seems I'm actually shouting my questions at her in some bizarre act of over-compensation. "Then I read the Vanity Fair piece [The Suspects Wore Louboutins by Nancy Jo Sales] and saw the kids' quotes, and it sounded like it had the elements for a fun pop movie. I also realised that what they did really took some ingenuity. These young people actually figured out how to do this thing and they had the guts to go through with it. I don't know if an adult would have figured that out. But also there was a deeper layer there to do with looking at celebrity culture now."

Alexis Neiers, the Bling Ring member who inspired Watson's character, decried the film as "trashy and inaccurate." "Her side of the story is very different," says Coppola. "I met with her but her version is that she was less involved. The kids' take was interesting to me though. When they were doing press and finally getting this celebrity status they had craved, they were a little bit delusional about why it was happening. Alexis wouldn't talk about the robbery: she seemed to think they were interviewing her because of her style or something. The boy was talking about how many Facebook followers he had gained. So I thought their perspective on it provided this whole other element which showed how wrapped up they were in celebrity. That part of our culture used to be small – that pop, 'guilty pleasure' side of things. Now it just won't stop growing." Part of her preparation involved speaking to some of the other people involved. "We talked to the boy and he told me that one of the girls wanted to steal Paris's dog, so we put that in the movie. I could never have thought up details like that."

Were you to adapt for the screen the experience of interviewing the director, it would fall uncomplicatedly into the second category of Sofia Coppola movie: after 40 minutes with her, I still feel I'm trapped on the outside trying to get in. Throw stones at her window and she politely draws the blinds. Jump and down, waving your arms demonstratively, and she transmits a weak smile of acknowledgment. Her handshake is so light it's like grasping air. Her most commonly used word, with which she begins most of her answers, or deflects questions she finds unappetising, is: "Oh." Soft as a marshmallow landing on a pillow; so quiet it might merely be a breath.

None of which can dampen an admirer's ardour. If you love Coppola's work, then it is likely to be this dazed, mildly anaesthetised atmosphere that has been a feature ever since The Virgin Suicides, with its dreamy shampoo-ad aesthetic and woozy Air soundtrack. Reserve functions so tantalisingly in her own films – it's the essence of her signature shot, the imperceptibly slow zoom into or out of a static, suspenseful tableau (Stephen Dorff alone in a makeup room in Somewhere, his entire head encased in plaster, or a wide exterior shot of one of the houses being robbed in The Bling Ring, each corner of the building lighting up as the thieves enter the different rooms). But that distance is also what scuppered her as a performer. Though she never had any aspirations to act, she was strong-armed by her father at the age of 18 into playing the substantial role of Michael Corleone's daughter in The Godfather Part III after the original choice, Winona Ryder, dropped out. The results were not pretty; nor were the reviews.

Sofia Coppola on the set of The Godfather III with her father Francis Ford Coppola Photograph: Alamy

When I press her on whether she wanted to do the film, she becomes visibly uncomfortable. "Do we have to talk about this – I mean, 20 years later?" she asks, making no effort to disguise her irritation. It's not exactly that the shutter lifts, more that there is a fleeting sense of what's behind it. Of course we have to talk about it, I tell her. After all, we've never met before; we've never discussed it. "Oh. OK. Let's see. Did I not wanna do it? Um. I was game. I was trying different things. It sounded better than college. I didn't really think about the public aspect of it. That took me by surprise. The whole reaction. People felt very attached to the Godfather films. I grew up with them being no big deal. I mean, I understand they're great films but … I dunno. I'm not surprised. It makes sense that people would have an opinion about it but I got a lot of attention I wasn't expecting. I was going to art school anyway so I was able to get back to what I was doing. It was before the internet so magazines would come out but then the next month they were gone. There wasn't even as much paparazzi around then."

She has left acting well enough alone since then, unless you count her appearances in a few music videos including the Chemical Brothers' Elektrobank, directed by her first husband, Spike Jonze (on whom the photographer in Lost in Translation is widely believed to be based). Or Funky Squaredance by Phoenix, the band in which Thomas Mars, her current husband and father of her two daughters, is vocalist. "I tried different things because, well, who knows what you'll connect with? I'm not a performer by nature. I'm not comfortable with it." There was also her cameo appearance as one of Queen Amidala's handmaidens in Star Wars Episode One: The Phantom Menace. "I mean, yeah, I was in it, but barely. I just wanted to visit the set. I know George [Lucas] from growing up near him and I thought, 'Oh, it'll be fun to be actually be on set but not be in the way.' I'm really just in the background." There seems little doubt it's her favourite place to be.

I ask if she lobbied for any of the upcoming Star Wars instalments. "You mean to direct one? Oh that's funny." She doesn't laugh. "Uh, no. It just sounds like a lot of pressure." I'd like to see a Sofia Coppola Star Wars film, I tell her. All the characters would probably be really bummed-out. She wrinkles her nose disapprovingly at that. "Oh. I hope not. I hope all my movies aren't like that."

But they are: wonderfully so. Slivers of enlightenment may come the way of her characters – though arguably not those in The Bling Ring, who end the movie imprisoned physically or metaphorically – but the mood is suffused with ennui and alienation. One of the new film's most dramatic moments, so understated that it is easy to miss, hinges on one character unfriending another on Facebook. "I'm glad you noticed because I wanted it to be a big deal. It's a real betrayal. I remember someone saying once that they'd been unfriended and even though I'm not on Facebook I could understand how upsetting that was." While some may see The Bling Ring's protagonists as dumb, superficial kids, Coppola's compassion shines through. "I like them," she says plainly. "They're not sympathetic. But they're really only misguided. And they're still young. They're getting all the culture in their lives from pop culture, which is sort of like having a bad diet."